Heralded non-destructive quantum entangling gate with single-photon sources

Heralded entangling quantum gates are an essential element for the implementation of large-scale quantum computation. Yet, the experimental demonstration of genuine heralded entangling gates with free-flying output photons in an all-optical system was hindered by the intrinsically probabilistic source and double-pair emission in parametric down-conversion. Here, by using an on-demand single-photon source based on semiconductor quantum dots and pseudo photon-number-resolving detectors, we demonstrate a heralded controlled-NOT (CNOT) operation between two single photons for the first time. To characterize the performance of the CNOT gate, we estimate its average quantum gate fidelity of ($87.8\pm1.2$)\%. As an application, we generated event-ready Bell states with a fidelity of ($83.0\pm2.4$)\%. Our results are an important step towards the development of photon-photon quantum logic gates.